Multimode fibers are successfully used in high-speed data networks together with high-speed sources that are typically using transversally multimode vertical cavity surface emitting lasers, more simply called VCSELs.
The Effective Bandwidth drives the performance of a system comprising a multimode fiber and a light source such as a VCSEL, and allows assessing the highest bit rate achievable and/or the longest reach achievable.
The Effective Bandwidth results from the combination of the modal dispersion and the chromatic dispersion.
Modal dispersion results from the fact that, in a multimode fiber, for a particular wavelength, several optical modes propagate simultaneously along the fiber, carrying the same information, but travelling with different propagation velocities. Modal dispersion is expressed in terms of Differential Mode Delay (DMD), which is a measure of the difference in pulse delay (ps/m) between the fastest and slowest modes traversing the fiber.
In order to minimize modal dispersion, the multimode optical fibers used in data communications generally comprise a core showing a refractive index that decreases progressively going from the center of the fiber to its junction with a cladding. In general, the index profile is given by a relationship known as the “α profile”, as follows:
            n      ⁡              (        r        )              =                            n          0                ⁢                              1            -                          2              ⁢                                                Δ                  ⁡                                      (                                          r                      a                                        )                                                  α                                                    ⁢                                  ⁢        for        ⁢                                  ⁢        r            ≤      a        ,
where:
n0 is a refractive index on an optical axis of a fiber;
r is a distance from said optical axis;
a is a radius of the core of said fiber;
Δ is a non-dimensional parameter, indicative of an index difference between the core and a cladding of the fiber; and
α is a non-dimensional parameter, indicative of a shape of the index profile.
When a light signal propagates in such a core having a graded index, the different modes experience a different propagation medium, which affects their speed of propagation differently. By adjusting the value of the parameter α, it is thus possible to theoretically obtain a group velocity, which is virtually equal for all the modes and thus a reduced intermodal dispersion for a particular wavelength. However, an optimum value of the parameter α is valid for a particular wavelength only. Furthermore, the exact parameter value α, as well as the actual shape of the refractive index profile, are difficult to control during manufacture of the fiber.
It is thus important to take account of modal dispersion when assessing the effective bandwidth of a multimode optical fiber link.
As mentioned above, the Effective Bandwidth is also affected by the chromatic dispersion, also called material dispersion. Chromatic dispersion occurs because the refractive index of a material changes with the wavelength of light. As a consequence, different wavelengths travel at different speeds in a multimode fiber. Since a pulse of light typically comprises several wavelengths, the spectral components of the optical signal spread in time, or disperse, as they propagate, causing the pulse width to broaden. A multimode fiber typically has a chromatic dispersion of the order of −100 ps/nm-km at a wavelength of 850 nm. The chromatic dispersion can vary between −80 and −120 ps/nm-km in the spectral range 840-860 nm.
Originally, modal and chromatic dispersions have been assumed to act independently. As a consequence, the Effective Bandwidth (EB), which corresponds to the bandwidth of the fiber when both the modal dispersion and the chromatic dispersion are taken into account, has long been assessed as the result of an independent combination of the Effective Modal Bandwidth (EMB), which corresponds to the bandwidth of the source-fiber pair when the chromatic dispersion is disregarded, and a Chromatic Dispersion Bandwidth (BWch).
More precisely, the Chromatic Dispersion Bandwidth is determined from the spectral width for the VCSEL, by taking account of the nominal value of the chromatic dispersion of the fiber. Actually, the chromatic dispersion is considered as not varying so much from fiber to fiber.
The Chromatic Dispersion Bandwidth is hence calculated as follows:
            BW      ch        =                                        0.187                          L              ·              σ                                ·                                    10              12                                                                                            (                                          D                      1                                        )                                    2                                +                                                      (                                          D                      2                                        )                                    2                                                                    ⁢                                  ⁢        with        ⁢                                  ⁢                  D          1                    =                                                                  S                0                            4                        ·                          [                                                λ                  c                                -                                                                            (                                              λ                        0                                            )                                        4                                                                              (                                              λ                        c                                            )                                        3                                                              ]                                ⁢                                          ⁢          and          ⁢                                          ⁢                      D            2                          =                  0.7          ·          σ          ·                      S            0                                ,
where:
L is the link length in kilometers;
σ is the root mean square (rms) optical spectral width of the laser source in nm;
λ0 is the wavelength of zero dispersion of the fiber in nm;
λc is the center wavelength of the laser;
S0 is the dispersion parameter of the fiber in ps/(km·nm)2.
As regards Effective Modal Bandwidth, it is usually estimated by a measurement of the delay due to the modal dispersion, known under the acronym DMD for “Dispersion Modal Delay” graphical representation. The DMD measurement procedure has been the subject of standardization (IEC 60793-1-49 and FOTP-220) and is also specified in Telecommunications Industry Association Document no. TIA-455-220-A. The DMD metric is expressed in units of picoseconds per meter (ps/m) so that the total delay is normalized by fiber length. Low modal dispersion as measured by DMD generally results in higher-bandwidth MMF.
A DMD graphical representation is obtained by injecting a light pulse having a given wavelength λ0 at the center of the fiber and by measuring the pulse delay after a given fiber length L; the introduction of the light pulse of given wavelength λ0 being radially offset to cover the entire core of the multimode fiber.
Once the Effective Modal Bandwidth and the Chromatic Dispersion Bandwidth have been assessed, the total bandwidth, also called Effective Bandwidth is calculated as follows:
  EB  =      1                            1                      EMB            2                          +                  1                      BW            ch            2                              
However, for relatively long reach and at high bit rate, and especially in case of transversally multimode sources, source and fiber do not drive the system performance independently, because of Modal and Chromatic Dispersion Interactions (MCDI).
Actually, the sources used in optical transmission systems are generally not monochromatic. Thus, the widely used VCSELs have a wide-spectrum discrete emission. The VCSELs used for high-speed transmissions are generally longitudinally but not transversally single mode, each transverse mode of the laser having its own wavelength corresponding to the various peaks of the emission spectrum. The emission spectrum thus has a spatial dependence.
When the optical signal emitted by the VCSEL is introduced into the multimode fiber, each transverse mode of the VCSEL will diffract differently: the transverse modes of the highest order diverge more rapidly due to their phase and the spatial distribution of their energy, they will therefore be coupled more specifically in the high order modes of the fiber. It will be recalled that the high order modes of the VCSEL occupy the lowest wavelengths in the spectrum. This spectral and spatial distribution of the VCSEL modes results in the highest order modes of the fibers mostly carrying the lowest wavelengths in the spectrum: the chromatic dispersion will therefore further delay the higher order modes relative to the delay of the fundamental mode.
The chromatic dispersion will thus introduce a modal dispersion referred to by the acronym MCDI for “Modal and Chromatic Dispersion Interferences”, resulting in a limitation of the bandwidth.
Document US 2011/0054861 A1 stresses the fact that the currently standardized algorithms for determining DMD and EMB, though adequate for appraising the quantitative amount of modal dispersion of a particular fiber at a particular measurement wavelength, do not correctly address both modal and chromatic dispersion effects, and discloses an improved algorithm for calculating the bandwidth of a particular laser transmitter and fiber combination, aiming at correctly combining both modal and chromatic dispersion effects.
According to this prior art document, a total bandwidth accounting for both chromatic and modal dispersions is assessed through the computation of a transfer function Hfiber(f,n), determined by deconvolving the launch reference pulse R(t) used in the DMD measurements, from the output temporal responses Pcd(t,n), as follows:Hfiber(f,n)=FT{Pcd(t,n)}/FT{R(t)}withPcd(t,n)=ΣrDcd(r,t,n)=Ucd(r,t)W(r,n)andUcd(r,t)=FT−1{FT{U(r,t)}·Hcd(f,r)}
where U(r,t) are the temporal responses of the multimode fiber optical cable, measured using spectrally narrow and temporally short pulses of light with central wavelength λc, injected into a core of the multimode fiber optic cable at series of radial offsets r from the core,
and where Ucd(f,r) is the chromatic dispersion transfer function calculated at the radial offset r from the Time Of Flight TOF(λ) and the optical spectrum of the transceiver measured at offset r L (λ,r):Hcd(f,r)=FT{L(λ,r)TOF(λ)}.
Although it attempts to take account of both modal and chromatic dispersion for characterizing a multimode fiber system, such a method shows several drawbacks.
First, such a method does not differentiate between the source characterization and the fiber characterization.
Secondly, such a method does not disclose how to use the source and fiber metrics to derive the Effective Bandwidth of a multimode optical fiber link, but only allows determining a bandwidth range, and perhaps a minimum bandwidth of a fiber and a population of laser transmitters.
Yet, the Effective Bandwidth value of a multimode optical fiber link is very useful to optimize the system performance, to assess its reach, to assess power penalties or a maximum bit rate achievable for example.
It would hence be desirable to have an improved method for assessing the effective bandwidth of a system comprising a source and a multimode fiber, which would take account of both chromatic and modal dispersion effects.
It would also be desirable to have such a method that does not require in situ measurements. It would also be desirable to obtain new metrics that would characterize the source and the multimode fiber, and that could be used to predict system performances.